Transient dynamics and early diagnostics in infectious disease

Abstract

To date, mathematical models of the dynamics of infectious disease have consistently focused on understanding the long-term behavior of the interacting components, where the steady state solutions are paramount. However for most acute infections, the longterm behavior of the pathogen population is of little importance to the host and population health. We introduce the notion of transient pathology, where the short-term dynamics of interaction between the immune system and pathogens is the principal focus. We identify the amplifying effect of the absence of a fully operative immune system on the pathogenesis of the initial inoculum, and its implication for the acute severity of the infection. We then formalize the underlying dynamics, and derive two measures of transient pathogenicity: the peak of infection (maximum pathogenic load) and the time to peak of infection, both crucial to understanding the early dynamics of infection and its consequences for early intervention.

A low dimensional dynamical model of the initial pulmonary innate response to infection

“…Much of the effort in modeling of immunity has been placed on long term dynamics and the adaptive system [3, 50, 2] and there has been limited focus on the onset of infection and initial response (for one such study see [34]). Further, we find very little mathematical modeling of the immune response in the lungs, except for an extensive and rich literature on M. tuberculosis infections (see [16, 30]).…”

Gastrointestinal helminths increase Bordetella bronchiseptica shedding and host variation in supershedding

“…We assumed that the three immune variables proportionately increase with the intensity of infection, y i (t), and neutralize B. bronchiseptica following a Lotka-Volterra type of relationship [47][48][49]. We also assumed that helminths affect B. bronchiseptica infection, and thus shedding, by altering the magnitude and time course of the neutrophil, IgA and IgG response.…”

Mathematical modelling of bacterial resistance to multiple antibiotics and immune system response

“…Mathematical models are one of the significant tools used in both analyzing the spread of infectious diseases in a population of individuals (Hethcote 2000 ; Singer 1984 ), and predicting the timing and expansion of infection and possible reinfection processes in an individual (Mohtashemi and Levins 2001 ). While the former is usually used for planning, prevention and control scenarios, the latter can be active in therapy/intervention programs for treating the individuals exposed to the particular pathogen.…”

“…Consequently, results on reproduction of sensitive and resistant bacteria to antibiotics are obtained in Austin et al ( 1997 ), Bonten et al ( 2001 ), Esteva et al ( 2011 ), Wiesch et al ( 2011 ), Zhang ( 2009 ); definitions of factors responsible for resistance prevalence are studied in Austin and Anderson ( 1999 ), Linares and Martinez ( 2005 ), Opatowski et al ( 2011 ), Rodrigues et al ( 2007 ); bacteria behavior under different antibiotic treatments is examined in Alavez et al ( 2006 ), Bonhoeffer et al ( 1997 ), Bootsma et al ( 2012 ), D’Agata et al ( 2007 ), Sun et al ( 2010 ); optimization results and design of control measures are investigated in Bonten et al ( 2001 ), Haber et al ( 2010 ), Massad et al ( 2008 ), Sotto and Lavigne ( 2012 ); biological cost and persistence of antibiotic resistance are analyzed in Andersson et al ( 2001 ), Andersson and Levin ( 1999 ), Antia et al ( 1996 ), Johnson and Levin ( 2013 ), Mondragón et al ( 2014 ); dynamics between pathogens and immune response are given in André and Gandon ( 2006 ), Carvalho et al ( 2012 ), D’Onofrio ( 2005 ), Gilchrist and Coombs ( 2006 ), Gilchrist and Sasaki ( 2002 ), Kostova ( 2007 ), Mohtashemi and Levins ( 2001 ), Nowak and May ( 2000 ), Whitman and Ashrafiuon ( 2006 ), respectively.…”